Model dependences of the deactivation of phytoplankton pigment excitation energy on environmental conditions inthesea*

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1 Model dependences of the deactivation of phytoplankton pigment excitation energy on environmental conditions inthesea* doi: /oc OCEANOLOGIA, 54(4), pp C Copyright by Polish Academy of Sciences, Institute of Oceanology, Open access under CC BY-NC-ND license. KEYWORDS Chlorophyll a fluorescence Marine photosynthesis Non-photochemical quenching of the chlorophyll a fluorescence Quantum yields of deactivation processes Mirosława Ostrowska Institute of Oceanology, Polish Academy of Sciences, Powstańców Warszawy 55, Sopot , Poland; ostra@iopan.gda.pl Received 7 August 2012, revised 19 September 2012, accepted 27 September Abstract A semi-empirical, physical models have been derived of the quantum yield of the deactivation processes(fluorescence, photosynthesis and heat production) of excited states in phytoplankton pigment molecules. Besides some already known models(photosynthesis and fluorescence), this novel approach incorporates the dependence of the dissipation yield of the excitation energy in phytoplankton pigment molecules on heat. The quantitative dependences of the quantum yields of these three processes on three fundamental parameters of the marine environment aredefined: thechlorophyllconcentrationinthesurfacewaterlayer C a (0)(the basin trophicity), the irradiance P AR(z) and the temperature temp(z) at the study site. The model is complemented with two other relevant models describing the quantum yield of photosynthesis and of natural Sun-Induced Chlorophyll a Fluorescence (SICF) in the sea, derived earlier by the author or with her * Support for this study was provided by the project Satellite Monitoring of the Baltic Sea Environment SatBałtyk funded by European Union through European Regional Development Fund contract No. POIG /09. The complete text of the paper is available at

2 546 M. Ostrowska participation on the basis of statistical analyses of a vast amount of empirical material. The model described in the present paper enables the estimation of the quantum yields of phytoplankton pigment heat production for any region andseason,inwatersofanytrophicityatdifferentdepthsfromthesurfaceto depthsofca60m. Themodelcanthereforebeusedtoestimatetheyieldsof these deactivation processes in more than half the thickness of the euphotic zone inoligotrophicwatersandinthewholethickness(anddeeper)ofthiszonein mesotrophic and eutrophic waters. In particular these relationships may be useful for a component analysis of the budget of light energy absorbed by phytoplankton pigments, namely, its utilization in fluorescence, photochemical quenching and nonphotochemical radiationless dissipation i.e. direct heat production. 1. Introduction 1.1. Presentation of the physical problem Phytoplankton cells in the sea and other water basins contain numerous sets of pigments, which we generally divide into photosynthetic pigments (PSP)(themainabbreviationsandsymbolsusedinthetextarelistedin the Annex, see page 563) and photoprotecting pigments(ppp)(goodwin 1952, 1965, Majchrowski 2001). When solar radiation reaches these cells it is spectrally selectively absorbed by the various pigments, which initially leads to the energetic excitation of the molecules. The excitation energy of the molecules of the pigments protecting the cells from excess light(ppp) is usually dissipated radiationlessly in that it is converted into heat that is then conducted to the cell s surroundings. On the other hand, the excitation energy of PSP is conveyed to chlorophyll a molecules, which use this energy to produce organic matter by photosynthesis. This energy is only partially consumed during photosynthesis, that is, for the assimilation of carbon. The portionthatisnotusedinthisprocessisradiatedintheformofchlorophyll fluorescenceinthespectralbandca685nm,and/orisalso(asinthecase of PPP) dissipated radiationlessly(by internal conversion and inter-system crossing), and is ultimately liberated in the form of heat. Among the above-mentioned ways in which the excitation energy of phytoplankton pigment molecules is dissipated as a result of light absorption, three groups of processes can be distinguished in nature that complement one another in such a way that their summed quantum yields areequaltoone. Thiscanbeexpressedasfollows(Kolber&Falkowski 1993): Φ fl + Φ ph + Φ H = 1, (1) where the symbols in equation(1) denote the quantum yields of: Φ fl fluorescence,thatistheratioofthenumberoflightquantainthe spectrabandat685nmemittedbychlorophyllatothetotalnumber

3 Model dependences of the deactivation of phytoplankton of quanta from different spectral bands of visible light, absorbed by all phytoplankton pigments(psp and PPP); Φ ph thephotochemicalreactionsinvolvedinthephotosyntheticassimilation of carbon; in other words, the number of quanta supplying energytothesereactionsto asabove thenumberofallquanta absorbed; Φ H directheatproduction, i.e. thenonphotochemicalradiationless dissipation of the excitation energy of pigments, both PPP and PSP, by way of internal conversion and inter-system crossing. By this yield weheremeantheratioofthenumberofquantadissipatedasheat(the difference between the number of quanta absorbed by all pigments andthesumofthenumberofquantaconsumedintheassimilation ofcarbonoremittedintheformofchlorophyllafluorescence)tothe number of all absorbed quanta The scientific objective of the analyses Thequantumyieldsofthethreeexcitationdissipationprocesses(Φ fl, Φ ph, Φ H ),takingplaceundernaturalconditionsintheseaorsomeother water body and their interrelationships, are diverse and depend on the environmental factors in the water body. Some of the dependences of the quantum yields of these three processes on environmental factors in different seas were studied empirically and mathematically modelled by various authors. Usually they focused on one of the three processes, such as photosynthesis(koblentz-mischke 1985, Morel 1991, Antoine et al. 1996, Antoine & Morel 1996, Ficek 2001) or the natural Sun-Induced Chlorophyll a Fluorescence(SICF)(e.g. Babin et al. 1995, Maritorena etal.2000,morrison2003,huotetal.2005,huotetal.2007).whatwas lacking was a model description of the quantum yield of heat production. Ontheotherhand,theyieldsofallthreegroupsofprocessesandthe relations between them were investigated experimentally, also using remote sensing methods(westberry& Siegel 2003). Even so, despite the many empirical studies carried out in different seas and oceans, no coherent statistical or model description has yet been developed for estimating both the absolute values and the relations between all three dissipation processes of phytoplankton pigment excitation energies in the sea. In view of the above, the present work was undertaken to derive a mathematical model of the dependence of the quantum yield of direct heat production by phytoplankton i.e. non-photochemical radiationless dissipation on the three principal environmental factors governing phytoplankton growthinthesea:thebasintrophicity C a (0),thelightconditionsatdifferent

4 548 M. Ostrowska depths in the water body under scrutiny (P AR(z)) and the temperature (temp)intheeuphoticzone. Withsuchamodelitwaspossibletoderive a full model. Achieving an objective formulated in this way is not a simple matter because the relevant set of empirical data required to establish the empirical constantsofsuchamodelandtovalidateitdoesnotexist. Thereason for this is that it is practically impossible to make direct measurements oftheheatproduction. Themostonecandoistotakesimultaneously definedempiricalquantumyieldsoffluorescence Φ fl andofphotosynthesis Φ ph and use them to calculate the yields of the heat production as valuescomplementarytotheunityofthesumofthequantumyieldsof fluorescence and photosynthesis, that is, on the basis of relationships that are rearrangements of equation(1). Unfortunately, I neither possess nor have been unable to find in the availableliteraturesuchdatacontainingyield Φ H indirectlydetermined empirically for different environmental conditions in the sea in quantities sufficient to make statistical generalizations. In this situation, to derive the model of the dependence of the heat production in the sea on environmental factors I have used two models that I developed independently or in cooperation with others, the successively updated versions of which were published in the reports mentioned below. These are models of two complementary means by which the excitation energies of pigment molecules in the photosynthetic apparatus are dissipated, namely, photosynthesis in the sea and the Sun-Induced Chlorophyll a Fluorescence(SICF) in the sea. These models and the results of the subsequent modelling performed on their basis will now be described. 2. Assumptions and mathematical apparatus of the model As already mentioned, the model description of the dependence of the heat production in the sea on environmental factors, presented in this work, is a kind of synthesis of two models that I developed earlier independently or with the cooperation of other scientists. The first is the model of photosynthesisintheseaand,inparticular,itsquantumyield Φ ph. It was developed successively, starting in 1992(Woźniak et al. 1992a,b, 1995, 2002, 2003, 2007, Dera 1995, Ficek 2000), and the latest synthetic version canbefoundinostrowska(2012). Thismodelisfoundedontheresults of statistical analyses of primary production measured in situ, and the basic environmental parameters governing this production(temperature, irradiance, chlorophyll concentration) in different trophic types of basins of theworldocean,thoughmainlyintheblackandbalticseas.theother modeliamgoingtouseinthisworkisthemodelofthequantumyield

5 Model dependences of the deactivation of phytoplankton ofthenaturalfluorescenceofchlorophyllainthesea Φ fl,whichihave been working on since 2009(Ostrowska 2010, 2011); the latest updated versionwillbefoundinostrowska(2012). Itisbasedontheresultsof statisticalanalysesoftheyieldofthisfluorescence Φ fl,indirectlydetermined empirically (on the basis of spectral measurements of the underwater fields of irradiance and radiation) and simultaneous measurements of the fundamental environmental factors governing this fluorescence in various regions of the Atlantic Ocean and Baltic Sea. Thesemodeldescriptionsenabletheabovequantumyields Φ fl (z)and Φ ph (z)tobeestimatedfromthethreemainenvironmentalparameters governing phytoplankton growth in the sea: basin trophicity, assumed to bethesurfaceconcentrationofchlorophylla, C a (0);thelightconditionsin thesea,theindexofwhicharevaluesoftheirradiance PAR(z)atvarious depths; and the temperature temp(z) at different depths. These models are based on empirical material collected in the surface layer of waters, i.e. from thesurfacedowntoadepthofca60m. Thisisequivalenttothewater massesinroughlyhalftheeuphoticzoneinbasinswith C a (0) < 1mgm 3, andalmostthewholeoftheeuphoticzoneoreventransgressingitin other basins. The measurements were carried out in basins of different trophicityandattemperaturesrangingfromca5 Ctoca30 C.Wecan therefore assume that the relationships are practically universal: to a good approximation they quantitatively describe the processes of photosynthesis and the natural fluorescence of phytoplankton in any ocean or sea basin. The modelling of the yields of heat processes presented in this work isbasedonthesameprinciplesastheabovemodelsoffluorescenceand photosynthesis. The appropriately modified assumptions of this modelling are as follows: Assumption 1: The model quantum yields of the heat production Φ H (z)at particulardepthsinthesea arecomplementary to the unityofthesumofthequantumyieldsofphotosynthesis Φ ph (z)and fluorescence Φ fl (z),asemergesfromequation(1). Assumption 2: The quantum yield of chlorophyll a fluorescence as well as the quantum yield of photosynthesis in marine phytoplankton can be described by the product of the theoretically maximum possible values of the yield of these processes and five dimensionless factors takingvaluesfrom0to1(woźniaketal.2007,ostrowska2012): Φ ph = Φ ph, MAX f a f f c(ca(0)) f c(parinh ) f E,t, (2) Φ fl, v = Φ fl, v, MAX f fl, a f fl, f fl, c(ca(0)) f fl, c(parinh ) f fl, E, t =

6 550 M. Ostrowska = Φ fl, v, MAX f a f (1 f c(ca(0)))f c(parinh ) (1 f E, t ), (3) where Φ ph,max = 0.125molatCEin 1 (or1einein 1 )isthetheoretically maximum possible value of the yield of photosynthesis; Φ fl, v, MAX = 1EinEin 1 isthetheoreticallymaximumpossiblevalue of the yield of fluorescence; f a, f fl, a afactoraccountingfortheeffectofnon-photosynthetic pigment absorption; it describes the decrease in the quantum yieldinrelationto Φ MAX duetothepresenceintheplantof photoprotecting pigments that do not transfer absorbed energy to the PS2 reaction centres(rc). The excitation energy of PPP isnottransferredtoareactioncentre,soitcannotbeusedin photosynthesisorberadiatedintheca685nmspectralbandby thechlorophyllapresentinthisrc.hence f fl, a = f a ; f, f fl, theinefficiencyfactorinenergytransferandchargerecombination. This describes the disruption to the functioning of photosynthetic RCs, causing the non-acceptance from pigments of excitation energy that could be further used for photosynthesis, orberadiatedintheformofchlorophyllafluorescenceintheca 685nmband.Therefore f fl, = f ; f c(ca(0)), f fl, c(ca(0)) afactordescribingtheinfluenceoftrophicity (i.e. thesurfaceconcentrationofchlorophylla, C a (0))onthe number of functioning centres for photosynthesis and fluorescence respectively. Basin trophicity affects the yields of photosynthesis andfluorescenceindifferentways,factor f fl, c(ca(0)),describing the dependence of the number of active PS2 RCs on basin trophicity,isaddedto f c(ca(0))toachieveunity.i.e. f fl, c(ca(0)) = 1 f c(ca(0)); f c,(parinh ), f fl, c(parinh ) afactordescribingthereductioninthe portion of functional PS2 RC as a result of photoinhibition. Since these centres are damaged by excess light energy, they do not take up energy that could then be used for the photosynthesis of organic matter or radiated in the form of chlorophyll a fluorescence in the ca 685 nm band. Hence f fl, c(parinh ) = f c(parinh ); f E,t afactordescribingtheclassicdependenceofphotosynthesis on light and temperature(morel 1991, Dera 1995, Ficek 2001 andthepaperscitedthere),alsoknownasthelightcurveof photosynthetic efficiency at a given temperature. It defines the

7 Model dependences of the deactivation of phytoplankton relative number of closed RCs, and hence is proportional to the quantum yield of photosynthesis; f fl, E, t afactordescribingthedependenceoffluorescenceonlight and temperature. The yield of the fluorescence is proportional totherelativenumberofopenrcs,so,factor f fl, E, t,addedto f E,t givesunity,i.e. f fl, E,t = 1 f E,t. The mathematical dependences of the above factors on the main environmental parameters governing phytoplankton established during empirical studies are given in Table 1(items 5 9). Assumption3:Onthebasisoftheresultsoftheworkofmanyauthors itisassumedthattherearetwocomponentsinthefluorescenceof chlorophyll a, making up the overall intensity of this fluorescence: theconstantcomponent F 0 andthevariablecomponent F v (seee.g. Kolber& Falkowski 1993, Matorin et al. 1996, Ostrowska et al. 2000, Ostrowska 2001). It is thus assumed that the formula for the quantum yieldoffluorescence Φ fl canalsobeexpressedasthesumofthetwo relevant component functions: Φ fl = Φ fl, 0 + Φ fl, v, (4) where Φ fl,0 is the quantum yield of the constant component of fluorescence F 0, while Φ fl, v is the quantum yield of the variable componentoffluorescence F v. Theconstantcomponentoffluorescence F 0 isalwayspresent,that is, regardless of whether at a given instant the photosynthetic reaction centresrcareopenorclosed. Ontheotherhand,thevariable component F v appearsonlywhenthercsareclosedandfluorescence is taking place instead of photosynthesis. Assumption4: Thequantumyieldoftheconstantcomponent Φ fl, 0 of the natural fluorescence of chlorophyll in a basin in daylight isafunctionofthesurfaceconcentration ofchlorophylla, C a (0) (and therefore depends on basin trophicity; Ostrowska 2012). The approximate form of this relationship, established as a result of the statistical analyses of numerous sets of empirical data, is given in Table1(item4). The set of equations, derived from assumptions 1 4, describing the modelsofthedependencesofthequantumyieldofheatproductioninthe sea on environmental factors, is given in Table 1.

8 552 M. Ostrowska Table1.Modelofthedependenceofthequantumyieldsofthedissipationof excited states in pigment molecules on environmental factors No. Basic equations 1 forfluorescence Φ fl = Φ fl,0 + Φ fl, v = Φ fl,0 + Φ fl, v,max f fl, a f fl, f fl, c(ca(0))f fl, c(parinh )f fl, E, t 2 forphotosynthesis Φ ph = Φ ph, MAX f a f f c(ca(0)) f c(parinh ) f E, t 3 forotherprocesses Φ H = 1 (Φ fl + Φ ph ) dissipating excited states No. Component and factors 4 Φ fl, 0 = C a(0) seebyostrowska(2012) ã pl = f(c a(0), τ, PAR(0)) 5 f a = ã pl,psp, where f ã fl, a = f a,where pl ã pl,psp = f(c a(0), τ) definitionof f aand descriptionof ã pland ã pl,pspsee Woźniak et al.(2007), f fl, a see Ostrowska(2012) 6 f ± f fl, = f,where f seewoźniaketal. (2007), f fl, see Ostrowska(2012) ( ) PAR 2 7 f c(parinh ) = exp, f fl, c(parinh ) = 8 f E, t = 2.23 temp/10 = f c(parinh ), where PAR = PAR(0)e τ where f c(parinh ) see Woźniak etal.(2007), f fl, c(parinh )see Ostrowska(2012) [ ( 1 exp PUR PSP temp/10 )] f fl, E, t = 1 f E, t, where f E, t see temp/10 PUR, Woźniak et al.(2007), PSP f fl, E, t see where PUR PSP = PAR ã pl,psp Ostrowska(2012)

9 Model dependences of the deactivation of phytoplankton Table1.Modelofthedependenceofthequantumyieldsofthedissipationof excited states in pigment molecules on environmental factors(continued) No. Basic equations where 9 f c(ca(0)) = C a(0) C a(0) 0.66 f fl, c(ca(0)) = 1 f c(ca(0)), where f c(ca(0))given by Woźniak et al.(1992a,b), f fl, c(ca(0))seeostrowska(2012) C a(0) totalchlorophyllaconcentrationinthesurfacewaterlayer[mgm 3 ], PAR downwardirradianceintheparspectralrange[µeinm 2 s 1 ], PUR PSP mass-specific radiation flux absorbed by photosynthetic pigments [µein(mgtot.chla) 1 s 1 ], temp ambientwatertemperature[ C], τ optical depth in the sea[dimensionless], ã pl, ã pl,psp [m 2 (mgtot.chla) 1 ] meanmass-specificcoefficientoflightabsorptionof all, and only photosynthetic(psp) pigments weighted by the irradiance spectrum respectively. 3. Modelling results; discussion The mathematical description of the relationship between the quantum yields of processes of the deactivation of phytoplankton pigment excitation energy and environmental factors, presented in this paper(see eqs. (2) (4) and Table 1), enables their variability under different conditions in the watercolumntobetrackeddowntoadepthofca60m. Onthisbasis Figure 1 illustrates the dependences of the quantum yields of all three sets of processes by which excited states in the molecules of all phytoplankton pigments are dissipated on the P AR irradiance in different trophic types ofwater. Apartfromthedependenceoftheyield Φ H (Figure1b),the figurealsoshowsthedependenceofthequantumyieldoffluorescence Φ fl (Figure1a)andthequantumyieldofphotosynthesis Φ ph (Figure1c). In order to compare the strongly differentiated ranges of variability of these three yields, their values are presented on a logarithmic scale. TheplotsinFigure1showthatheatproductionisthemosteffective of the three possible ways of quenching excited states of PSP molecules inthesea. Thequantumyieldofheatproductionfarexceedstheother two forms of dissipation in practically all possible configurations of the principalenvironmental parameters. Values of the quantumyield Φ H usuallystartfromca0.65andinsomecases(seethediscussionbelow) canrisetoalmost1(figure1b). Forthesametrophictypesofwaters

10 554 M. Ostrowska Figure 1.Dependenceofthemodelquantumyieldsof: fluorescence Φ fl (a), directheatproduction Φ H (b),photosynthesis Φ ph (c)ontheunderwater irradiance P AR in different trophic types of basins with surface chlorophyll a concentrations C a (0)varyingfrom0.035to7mgm 3,forasurfacedownward irradiance PAR = 1500 µeinm 2 s 1 and temp = 15 C.(Calculatedbymeansof themodelformulasgivenintable1) theyarethusfromca20to150timesgreaterthanthequantumyieldsof fluorescence Φ fl (Figure1a)andusuallyfrom2toca10timesgreaterthan thequantumyieldsofphotosynthesis Φ ph (Figure1c),wherebyinthelatter casethedependencesofquantumyields Φ H and Φ ph onbasintrophicity C a (0)areopposed: Φ H decreaseswithincreasing C a (0),while Φ ph risesas C a (0)doesso.Therearetwofurtherimportantfeaturesdistinguishingthe dependences of these three quantum yields on the environmental parameters under scrutiny here. The first one refers to the relative ranges of variability of the three quantum yields under natural conditions in the sea. The yields of fluorescence and photosynthesis vary within quite wide ranges: about oneorderofmagnitudeinthecaseof Φ fl andabouttwoordersinthecase of Φ ph. Incontrast,thechangesin Φ H aresmall,evenlessthantwofold. The second feature refers to the directions of their changes as the irradiance conditions change. At low levels of irradiance, over a broad range all three yields remain practically constant, that is, they are independent of the irradiance. At somewhat higher irradiance values(especially starting from ca PAR = 10 µeinm 2 s 1 ) Φ H and Φ fl increaseastheirradiancedoes so;butinthecaseof Φ fl thisincreaseisinhibited,andaboveirradiances intherangeca µeinm 2 s 1 valuesof Φ fl fall,whereas Φ H not

11 Model dependences of the deactivation of phytoplankton onlydoesnotfallbutcontinuestorisestrongly,almosttothemaximumof Φ H = 1.Ontheotherhand, Φ ph inmediumandhighirradianceintervals drops monotonically and ever more strongly with increasing P AR. On the other hand the specific nature of the relationship between the quantumyieldofheatproduction Φ H andenvironmentalfactorsismore preciselyillustratedinfigure2,inwhichthechangesinthevaluesof Φ H are shown on a linear scale. These plots represent the model dependences of this yield on the light conditions in different trophic types of water, where surfacechlorophyll C a (0)variesfrom0.035to7mgm 3 (a),thesurface irradiance PARvariesfrom300to1500 µeinm 2 s 1 (b),and tempvaries from5to30 C(c). As can be seen, the quenching of excited states of phytoplankton pigment molecules is particularly intense under conditions enabling the photoinhibition of the photosynthetic apparatus of algae; it is also triggered by other stress factors. This means that this increase is characteristic of all trophic types of water and at the various possible temperatures in the water under conditions when P AR reaches its highest possible values(in surface waters), where photoinhibition is particularly intense. This is due, among other things, to the presence of short-wave radiation known as Potentially Destructive Radiation(PDR), i.e. radiation in the spectral interval λ < 480 nm, especially that radiation readily absorbed by chlorophyllainthesoretband. Thisproblemisdiscussedindetailin Woźniak& Dera(2007). Chlorophyll molecules excited in this way have a good chance of shifting from the singlet state to the long-lived triplet state, which enhances the probability of their coming into contact with moleculesofoxygeno 2 andbeingphoto-oxidized.toprotectitselffromsuch an eventuality, a plant synthesizes photoprotecting carotenoids, whose role it is to capture this excitation energy of chlorophyll molecules and then to dissipate it in a radiationless manner, which increases the quantum yield of heatproduction Φ H.Theprincipalcompoundamongthephotoprotecting carotenoids is zeaxanthin, which is formed from violaxanthin in the socalled xanthophyll cycle(ruban& Horton 1999). The xanthophyll cycle consistsofawholesetofprocesses,yettobefullyunderstood,inwhich mutual conversions of membrane xanthophylls take place in the thylakoids, especially the conversion of violaxanthin to zeaxanthin. The current state of knowledge of this problem is analysed in detail in the papers by Morosinotto etal. (2003),Latowskietal. (2004),Standfussetal. (2005)andGrzyb etal.(2006).

12 556 M. Ostrowska Figure 2. Dependence of the model of quantum yield of direct heat production yield Φ H (calculatedonthebasisofthemodelasgivenintable1)onthe underwater irradiance P AR in different trophic types of(continued on next page)

13 Model dependences of the deactivation of phytoplankton Figure2.(continued)basinswithsurfacechlorophyll aconcentrations C a (0)varyingfrom0.035to7mgm 3 :forasurfaceirradiance PAR = 1500 µeinm 2 s 1 and temp =15 C(a);forasurfaceirradiance PARvaryingfrom300to1500(every300) µeinm 2 s 1 and temp = 15 C(b);fordifferenttemperaturesintheseavarying from5to30(every5) Candasurfaceirradiance PAR = 1500 µeinm 2 s 1 (c) ThegraphsshowninFigure2mayalsosuggestthatthisquantumyield is dependent not only on natural irradiance but also on other environmental parameters. These are: adecreaseinyield Φ H withincreasingbasintrophicity C a (0),visible onalltheplotsinfigure2intheintervalsofmediumandlow PAR irradiances; adistinctvariabilityinthevaluesofyield Φ H dependentonthe temperatureinthesea,intheintervalsoflowandmediumlevelsof P AR irradiances(see Figure 2c). This variability depends on a small dropinthevalueof Φ H withincreasingtemperatureineutrophic waters(plotfor C a (0) = 7mgm 3 infigure2c)andviceversa,on acontinuousmonotonicincreasein Φ H withrisingtemperaturein oligotrophicbasins(plotfor C a (0) = 0.035mgm 3 infigure2c). It should be noted, however, that the variability in the quantum yield of heatproduction Φ H associatedwiththebasintrophicity C a (0)atmedium and low irradiances is small. These quantum yields most frequently lie withinthelimitsfrom 0.7 Φ H 0.9,andhenceinanarrowrangeofvalues with a half-width of roughly 20%. This also applies to the second feature ofthevariabilityin Φ H,thatis,itsmodeldependenceontemperature.We anticipate, therefore, that these features may be encumbered by errors due totheinaccuracyofthemodelderivedandpresentedinthispaper. It was not developed on the basis of a statistical analysis of direct empirical measurements but indirectly, using two other model descriptions those ofthequantumyieldofphotosynthesisintheseaandthequantumyield of chlorophyll a fluorescence. These discrepancies, as already mentioned, mayrelateespeciallytothemodelledchangesintheyield Φ H causedby changes in trophicity and water temperature. Nevertheless, as shown above, themodeldescriptionofthedependencesof Φ H iscorrectandphysically justified. 4. Final remarks and conclusion Theaimofthisworkwastomodelthequantumyieldofheatproduction(i.e. nonphotochemical radiationless dissipation) by phytoplankton pigmentsinordertoobtainafulldescriptionofthedependencesofthe

14 558 M. Ostrowska deactivation of phytoplankton pigment excitation energy on environmental conditions in the sea. The end result can be regarded as satisfactory, given the current state of knowledge of the functioning of plant communities in thesea.amodelwasderived(seetable1)enablingquantumyieldstobe estimated from values of three basic environmental factors governing the growthofphytoplanktoninthesea,i.e. basintrophicity C a (0),andthe downward irradiance P AR(z) and the water temperature temp(z) at the study site. The model should be regarded as a preliminary version, for two reasons: 1.Inviewofthelackofempiricaldatacontainingtheyields, Φ H were determined in an indirect empirical manner for various environmental conditions in the sea in numbers sufficient for the statistical generalizations to be meaningful. The model was thus developed in the indirectwaydescribedinsection2,withtheaidoftwomodelsofthis type that I had derived earlier, either independently or in cooperation with others, namely, the model of natural fluorescence SICF and the modelofphotosynthesisinthesea. Butderivingsuchamodelof the quantum yield of the heat production by phytoplankton pigments fromdirectlydeterminedempiricalvaluesof Φ H requiressuchdatato be gathered in amounts sufficient for making the requisite statistical generalizations. Further research in this direction is needed and is being planned. 2. For the same reasons as given above(no empirical material available), this model was not validated to a sufficient degree with empirical dataandsotheaccuracyofthequantumyield Φ H estimatedusing this model was not assessed. Nonetheless, a number of circumstances indicate that the model is substantially correct, that is, up to 15 20%oftheestimatedyields. Oneofthemisrepresentedbythe verticalprofilesofthequantumyieldsofsicf(φ fl )(see Figure3a), andofphotosynthesis(φ ph )(see Figure3b)obtaineddirectlyfrom relevant empirical investigations in the Baltic, and the quantum yield ofheatproduction(φ H )(see Figure3c),obtainedindirectly(as acontributiontounity seeeq. (3))fromempiricalvaluesof Φ fl and Φ ph. Theplotsinthisfigureshowboththeabsoluteyield Φ H and the nature of its variability with irradiance, which decreases with increasing depth; they correspond to the modelled regularities (seefigures1and2)governingthechangesinthequantumyield Φ H causedbychangesin PARirradianceinthesea. Likewise,the natureofthespatialvariationsin Φ H overmanyseasonsin , investigated in the north-western Sargasso Sea and presented intheformofgraphsinwestberry&siegel(2003)resemblesto

15 Model dependences of the deactivation of phytoplankton Figure 3. Vertical profiles of the averaged quantum yields(and their standard deviations) of three processes taking place in phytoplankton cells: a) the natural fluorescence of chlorophyll a, b) photosynthesis, and c) direct heat production. These relationships were worked out for 13 measurement stations in different regions of the Baltic in (after Woźniak& Tyszka 2006 unpublished report) a significant extent the modelled regularities described in the present paper. Regardless of these favourable circumstances, however, the modelwillhavetobeproperlyvalidated,asubjectwhichiwillnow be focusing on. Described set of these three models used simultaneously can be used to balance the quantum yields of the deactivation of the excited states of moleculesofallpigmentsorjustchlorophyllainthesea.thiswillbeapplied in the next work, the aim of which will be to characterize quantitatively the quantum yields of the chlorophyll a fluorescence and its quenchings in differentmarinesystemoftheworldocean(seeostrowskaetal.(2012) in this volume). References Antoine D., Andre J. M., Morel A., 1996, Oceanic primary production: 2. Estimation at global scale from satellite (Coastal Zone Color Scanner) chlorophyll, Global Biogeochem. Cy., 10(1), 56 69, 95GB BabinM.,TherriaultJ.C.,LegendreL.,NiekeB.,ReuterR.,CondalA.,1995, Relationship between the maximum quantum yield of carbon fixation and the minimum quantum yield of chlorophyll a in vivo fluorescence in the Gulf of St. Lawrence, Limnol. Oceanogr., 40(5), , lo Dera J., 1995, Underwater irradiance as a factor affecting primary production, Diss. and monogr., 7, Inst. Oceanol. PAS, Sopot, 114 pp.,(in Polish).

16 560 M. Ostrowska Falkowski P.(ed.), 1980, Primary productivity in the sea, Env. Sci. Res., 19, Plenum Press,NewYork,531pp. Ficek D., 2001, Modelling the quantum yield of photosynthesis in various marine systems, Diss. and monogr., Inst. Oceanol. PAS, Sopot, 224 pp.,(in Polish). Ficek D., Majchrowski R., Ostrowska M., Woźniak B., 2000, Influence of nonphotosynthetic pigments on the measured quantum yield of photosynthesis, Oceanologia, 42(2), Goodwin T. W., 1952, The comparative biochemistry of the carotenoids, Chapman andhallltd.,london,336pp. Goodwin T. W., 1965, Chemistry and biochemistry of plant pigments, Acad. Press, London, 583 pp. Grzyb J., Latowski D., Strzałka K., 2006, Lipocalins a family portrait, J. Plant Physiol., 163(9), , HuotY.,BrownC.A.,CullenJ.J.,2005,NewalgorithmsforMODISsun-induced chlorophyll fluorescence and a comparison with present data products, Limnol. Oceanogr. Meth., 3, , Huot Y., Brown C. A., Cullen J. J., 2007, Retrieval of phytoplankton biomass from simultaneous inversion of reflectance, the diffuse attenuation coefficient and Sun-induced fluoresence in coastal waters, J. Geophys. Res., 112, C06013, 26 pp., Koblentz-Mishke O. I., Woźniak B., Ochakovskiy Yu. E., 1985, Utilisation of solar energy in the photosynthesis of the Baltic and Black Sea phytoplankton, Izd. Inst. Okeanol. AN SSSR, Moscow, 336 pp.,(in Russian). Kolber Z., Falkowski P. G., 1993, Use of active fluorescence to estimate phytoplankton photosynthesis in situ, Limnol. Oceanogr., 38(8), , Latowski D., Grzyb J., Strzałka K., 2004, The xanthophyll cycle Molecular mechanism and physiological significance, Acta Physiol. Plant., 26(2), , Majchrowski R., 2001, Influence of irradiance on the light absorption characteristics of marine phytoplankton, Diss and monogr., 1, Pom. Akad. Pedagog., Słupsk, 131pp.,(inPolish). Maritorena S., Morel A., Gentili B., 2000, Determination of the fluorescence quantum yield by oceanic phytoplankton in their natural habitat, Appl. Optics, 39(36), , MatorinD.N.,VenediktovP.S.,KonevYu.N.,KazemirkoYu.V.,RubinA.B., 1996, Application of a double-flash, impulse, submersible fluorimeter in the determination of photosynthetic activity of natural phytoplankton, Trans. Russ. Acad. Sci. Earth Sci. Sec., 350(7), Morel A., 1991, Light and marine photosynthesis: a spectral model with geochemical and climatological implications, Prog. Oceanogr., 26(3), , doi.org/ / (91)

17 Model dependences of the deactivation of phytoplankton Morosinotto T., Caffarri S., Dall Osto L., Bassi R., 2003, Mechanistic aspects of the xanthophyll dynamics in higher plant thylakoids, Physiol. Plantarum, 119(3), , Morrison J. R., 2003, In situ determination of quantum yield of phytoplankton chlorophyll a fluorescence: A simple algorithm, observations, and a model, Limnol. Oceanogr., 48(2), , Ostrowska M., 2001, The application of fluorescence methods to the study of marine photosynthesis, Diss. and monogr., Inst. Oceanol. PAS, 15, Sopot, 194 pp.,(in Polish). Ostrowska M., 2010, Dependence of quantum yield of chlorophyll a fluorescence in the sea on environmental factors the preliminary results, Ocean Optics XX, Conf. Proc., Anchorage. Ostrowska M., 2011, Dependence between the quantum yield of chlorophyll a fluorescence in marine phytoplankton and trophicity in low irradiance level, Opt. Aplicata, 41(3), Ostrowska M., 2012, Model of the dependence of the sun-induced chlorophyll a fluorescence quantum yield on the environmental factors in the sea, Opt. Express, 20(21), , Ostrowska M., Majchrowski R., Matorin D. N., Woźniak B., 2000, Variability of the specific fluorescence of chlorophyll in the ocean. Part 1. Theory of classical in situ chlorophyll fluorometry, Oceanologia, 42(2), Ostrowska M., Woźniak B., Dera J., 2012, Modelled quantum yields and energy efficiency of fluorescence, photosynthesis and heat production by phytoplankton in the World Ocean,(in this volume). Ruban A. V., Horton P., 1999, The xanthophyll cycle modulates the kinetics of nonphotochemical energy dissipation in isolated light-harvesting complexes, intact chloroplasts, and leaves of spinach, Plant. Phys., 2(119), Standfuss J., Terwisscha van Scheltinga A. C., Lamborghini M., Kühlbrandt W., 2005, Mechanisms of photoprotection and nonphotochemical quenching in pea light-harvesting complex at 2.5 Å resolution, EMBO J., 24(5), , Steemann Nielsen E., 1975, Marine photosynthesis, with special emphasis on the ecological aspect, Elsevier, Amsterdam-New York, 141 pp. Westberry T. K., Siegel D. A., 2003, Phytoplankton natural fluorescence variability in the Sargasso Sea, Deep-Sea Res. Pt. I, 50(3), , /S (03) Woźniak B., Dera J., 2007, Light absorption in sea water, Springer, New York, 452 pp. Woźniak B., Dera J., Ficek D., Majchrowski R., Ostrowska M., Kaczmarek S., 2003, Modelling light and photosynthesis in the marine environment, Oceanologia, 45(2),

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19 Model dependences of the deactivation of phytoplankton Annex Listoftheabbreviationsandsymbolsusedinthetext Symbol Denotes Units a Coefficientoflightabsorption m 1 a pl Coefficientoflightabsorptionby m 1 phytoplankton ã pl Meanabsorptioncoefficientforall m 1 phytoplankton pigments weighted by the irradiance spectrum ã pl Meanmass-specificabsorptioncoefficient m 2 (mgtot.chla) 1 for all pigments weighted by the irradiance spectrum ã pl,psp Meanmass-specificabsorptioncoefficientof m 2 (mgtot.chla) 1 photosynthetic pigments weighted by the irradiance spectrum C a Concentrationoftotalchlorophylla(i.e. mgtot.chl am 3 sumofchlorophyllsa+pheoderived spectrophotometrically) f a, f fl, a Non-photosyntheticpigmentabsorption dimensionless factor f fl, f fl, Inefficiencyfactorinenergytransferand dimensionless charge recombination f c(ca(0)), Factordescribingtheeffectofsurface f fl, c(ca(0)) chlorophyllaconcentrationonthe portion of functional PS2 RC for photosynthesis and fluorescence respectively dimensionless f fl, c(parinh ) Factorsdescribingthereductioninthe dimensionless portionoffunctionalps2rcasaresult of photoinhibition f E, t Classicdependenceofphotosynthesison dimensionless light and temperature also known as the light curve of photosynthesis efficiency at a given temperature f fl, E, t Factordescribingtheeffectofirradiance dimensionless and temperature on phytoplankton fluorescence F 0 Constantfluorescence arbitraryunits F v Variablefluorescence arbitraryunits PS2 RC PAR Reaction Centre in photosynthetic apparatus Photosynthetically Available Radiation

20 564 M. Ostrowska List of the abbreviations and symbols used in the text(continued) PAR PAR(0) DownwardirradianceinthePARspectral µeinm 2 s 1 range( nm) DownwardirradianceinthePARspectral µeinm 2 s 1 range( nm) just below the surface PURPSP Numberofquantaabsorbedbyphoto- µein(mgtot.chla) 1 s 1 synthetic pigments in unit time referred tounitmassofchlorophylla SICF Sun-Induced Chlorophyll a Fluorescence temp Ambient water temperature z Realdepthsinthesea m τ Optical depth in the sea dimensionless λ Wavelength of the light nm Φ ph Quantumyieldofphotosynthesis molatcein 1 or molcein 1 Φ fl Quantumyieldoffluorescence EinEin-1i.e. dimensionless Φ fl, 0 Φ fl, v Φ H Φ ph, MAX Φ fl, v,max Quantumyieldoffluorescence,associated EinEin 1 i.e. withtheconstantfluorescence F 0 dimensionless Quantumyieldoffluorescence,associated EinEin 1 i.e. withthevariablefluorescence F v dimensionless Quantumyieldofdirectheatproduction, EinEin 1 i.e. i.e. the nonphotochemical radiationless dissi- dimensionless pation of the excitation energy of pigments Theoreticalmaximumpossiblequantum atomcquanta 1 or yieldofphotosynthesis molcein 1 Theoreticalmaximumpossiblequantum EinEin 1 i.e. yield of fluorescence dimensionless C